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June
Pension and Tax:Designate a tax representative and ask them to file it at the local tax office.

Home Phone: Your home phone can be disconnected on a requested date but payment cannot be made at that time. Fees should be paid at your local NTT office of from you bank account at a later date. You can also ask someone to take care of it for you.

Mail: You can request mail be forwarded to an address in Japan if you complete a Change of Address Notification Form (てんきょとどけ）

Apartment: Landlords and rental agencies usually need to be informed at least a month in advance about moving out. If you know when you're leaving contact them now. They might arrange an apartment inspection and calculate prorated costs if you plan to stay only part of a month. Deposits will probably not be returned. Check with your landlord to find out.

Budgeting for Moving: 2 Months (suggested by the CLAIR After JET Guide)

Car: "Situation 1: Dispose of your car (haisha)
Situation 2: Sell your car "

Car Insurance: Call your company to find out about the cancellation process

Shipping: The sooner the better

Visa: "Situation 1: Visa expires before your contract ends (Up to 2 months before your visa expires, appyy for an Extension of Period of Stay. This visa generally lasts from 6 months to 1 year.
Situation 2: Visa continues after contract expires and you stay in Japan (You can stay up to 90 days for the purpose of sightseeing in Japan after your contract finishes without changing your visa. After that, unless your new job falls under the category of your current visa, you must change your visa status. This visa is valid for either 90 days or 15 days.)
Situation 3: Visa expires on the same day or after your contract ends but before you leave Japan (Up to 2 weeks before your visa expires, apply for a Temporary Visa to begin from the day after your current visa expires.)"

July
TV & Cable: Call about a month in advance to find out the cancellation process for your company

Electricity: Call them a few days in advance and tell them the date of your departure. They will check your meter and ask you to pay the last bill in cash the day you leave.

Gas: Call them a few days in advance and tell them the date of your departure. They will check your meter and ask you to pay the last bill in cash the day you leave.

Water: Call them a few days in advance and tell them the date of your departure. They will check your meter and ask you to pay the last bill in cash the day you leave.

Last few days
Bank & Post Account: Take your account book, bank card, and inkan to the branch office and close the account (こうざかいやく）。 You cannot close your account from overseas.

Last Day
Cell: You can cancel at the airport AU, Docomo, Softbank. You'll need your alien registration card and passport and your cell phone. It may take up about an hour to calculate your costs and if you have already closed your Gunma bank account, you'll have to pay in cash.

Foreigner's Card: Turn this in at immgration if you want to get your pension refund